𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Rational Geometry of Conic Sections

✍ Scribed by Graziano Gentili; Michael A. O’Connor

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
282 KB
Volume
29
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis

Simple geometric objects and transformations appear in representations and algorithms of geometric facilities in computer applications such as modelling, robotics, or graphics. Usually, these applications only support objects and transformations fully describable by rational parameters, and a computer display of points of the objects at least implicitly requires points with rational coordinates. In this setting we investigate some basic questions of the geometry of rational conic sections, when the geometry is defined by the group of rational projective transformations, the group of rational affine transformations, or the group of rational rigid transformations. Some results follow classical results, while others turn out to be quite different. In particular, we obtain a complete classification scheme for nondegenerate rational conics for rational affine geometry and a constructive method for production of a minimal set of representatives of all equivalence classes.

📜 SIMILAR VOLUMES

On the Geometries of Conic Section Repre
On the Geometries of Conic Section Representation of Noisy Object Boundaries
✍ Qiuming Zhu 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 382 KB

This paper studies some geometrical properties of conic sections and the utilization of these properties for the generation of conic section representations of object boundaries in digital images. Several geometrical features of the conic sections, such as the chord, the characteristic point, the gu

On Equalizers of Sections
On Equalizers of Sections
✍ Warren Dicks; M.J Dunwoody 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 157 KB

Let G and M be groups, and a, b: G ª G) M group-theoretic sections of the natural projection G) M ª G. We use the Almost Stability Theorem, pro-trees, and new folding sequence techniques to show that if G is finitely generated, then the equalizer of a and b is a free factor of G, which answers a que

Search for optimal geometry of a conical
Search for optimal geometry of a conical turbine agitator for heat transfer in stirred vessels
✍ Prof. Dr. hab. inz. Frederyk Strek; Dr. Inz. Joanna Karcz; Dr. Inz. Waldemar Buj 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 650 KB

Simultaneous measurements of power consumption P and heat transfer coefficient CY for a jacketed, baffled, agitated vessel of diameter D = 0.45 m, equipped with a conical turbine, were carried out. The following geometric parameters of the agitator were tested: diameter d , blade width b and number